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arXiv · 1811.12163

Milnor-Witt Cycle Modules

Niels Feld
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Abstract

We generalize Rost's theory of cycle modules using Milnor-Witt K-theory instead of the classical Milnor K-theory. We obtain a (quadratic) setting to study general cycle complexes and their (co)homology groups. The usual constructions are developed: proper pushfoward, (essentially) smooth pullback, long exact sequences, (coniveau) spectral sequences and products, as well as the homotopy invariance property; in addition, Gysin morphisms for lci maps are constructed. We prove an adjunction theorem linking our theory to Rost's.

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Niels Feld. 2020-04-30. Milnor-Witt Cycle Modules. https://arxiv.org/abs/1811.12163

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